I have been in nantucket with a good friend who introduced me to two great places .
Black Eyed Susan's
it is an exciting food & experience ,it is a small place and very popular with locals.
But it is very hard to get a reservations ( I did not made them but my friend told me )
the number 508/325-0308
another great place is Topper's at The Wauwinet
it is very old and very very delicious restaurant, if you can you must try their Lobster ( which is sautéed with champagne )
508/228-8768
enjoy